Question

Search study: Do red uniform wearers tend to win more often than those wearing blue uniforms in

Taekwondo matches where competitors are randomly assigned to wear either a red or blue uniform?
In a sample of 80 Taekwondo matches, there were 45 matches where the red uniform wearer won.
(A) What is the parameter of interest for this study?
(i) The long-run proportion of Taekwondo matches in which the red uniform wearer wins
(1) The proportion of matches in which the red uniform wearer wins in a sample of 80
Taekwondo matches
(ii) Whether the red uniform wearer wins a match
(iii) 0.50
(B) What is the statistic for this study?
(i) The long-run proportion of Taekwondo matches in which the red uniform wearer wins
(1) The proportion of matches in which the red uniform wearer wins in a sample of 80
Taekwondo matches
(ii) Whether the red uniform wearer wins a match
(iii) 0.50
(C) Given on the right is the simulated distribution of
the number of "red wins" that could happen by
chance alone in a sample of 80 matches.
Based on this simulation, is our observed result
statistically significant?
(i) Yes, since 45 is larger than 40.
(ii) Yes, since the height of the dot plot above 45
is smaller than the height of the dot plot above
40.
(iii) No, since 45 is a fairly typical outcome if the
color of the winner's uniform was determined by chance alone.)
(iv) No, since we could have observed a value greater than 45 just by random chance.

Answer 1

(A) (i) The long-run proportion of Taekwondo matches in which the red uniform wearer wins

(B) (i) The proportion of matches in which the red uniform wearer wins in a sample of 80 Taekwondo matches

(C) (iii) No, since 45 is a fairly typical outcome if the color of the winner's uniform was determined by chance alone.